Proportions in Triangles GEOMETRY LESSON 8-5 Pages 448-452 Exercises 1. 7.5 2. 8 3. 5.2 4. d 5. c 6. b 7. d 8. 7.5 9. 3 10. 9.6 11. 6 12. 4.8 13. 35 14. 3.6 15. 16. 12 1 3 40 7 17. KS 18. SQ 19. JP 20. KP 21. KM 22. PM 23. JP 24. LW 8-5

Proportions in Triangles GEOMETRY LESSON 8-5 25. 559 ft 26. 671 ft 27. 3.8 cm and 9.2 cm 28. Answers may vary. Sample: 9 cm and 13.5 cm 29. x = 18 m; y = 12 m 30. a. b. isosceles; - Bisector Thm. 31. 20 32. 2.5 33. 9 34. a. b. c. = 35. Measure AC, CE, and BD. Use the Side-Splitter Thm. Write the proport. = and solve for AB. 36. 4.5 cm or 12.5 cm 37. 6 38. 2.5 39. 19.5 40. h = 10.0, h1 = 4.3, h2 = 5.7 41. h = 13.0, 1 = 5.3, 2 = 11.9 42. 1 = 5.0, h1 = 3.8, h2 = 9.2 AB BC WX XY AC CE BD 8-5

Proportions in Triangles GEOMETRY LESSON 8-5 47. 1. Given 2. Prop. of Proportions 3. Segment Add. Post. 4. Reflexive Prop. of 5. SAS ~ Thm. 6. Corr. of ~ are . 7. If corr. are , lines are ||. 48. Yes; since = , the segments are || by the Converse of the Side-Splitter Thm. 49. No; . 50. Yes; since = , the segments are || by the Converse of the Side-Splitter Thm. x y s 6 10 9 15 28 12 24 20 16 43. 2 = 7.1, h2 = 5.0, h = 10.0 44. h = 17.0, h1 = 11.1, h2 = 5.9 45. h2 = 4, 1 = 5.7, 2 = 5.7 46. The ratio of the legs of a 30°-60°-90° is 3. Let the rt. bisector divide the hyp. into segments x and y. Then by the - - Bis. Thm., = 3, so x = 3 y. = / 8-5

Proportions in Triangles GEOMETRY LESSON 8-5 51. (continued) 1.  ABCD (Given) 2.  AE || BF and ED || FC (Def. of ) 3. AD BC (Opp. sides of are .) 4. E and F are midpts. of AD and BC. (Given) 5. AE = ED = AD; BF = FC = BC (Def. of midpt.) 6. AE = BF, ED = FC (Subst.) 7. ABFE and EFCD are (If one pair of opp. sides of a quad. is and ||, it is a .) 8. AB || EF and EF || CD (Opp. sides of a are ||.) 51. a. A midsegment of a connects the midpts. of 2 opp. sides. Given: ABCD with EF connecting the midpts. of AD and BC Prove: AB || EF; EF || CD 1 2 s b. 8-5

Proportions in Triangles GEOMETRY LESSON 8-5 51. (continued) c. Given: ABCD with midsegment EF Prove: EF bisects AC and BD. Since AB || EF || DC by part (b), and EF bisects AD, by the Side-Splitter Thm., EF bisects AC and BD. 52. D 53. F 54. [2]  = ; 35n + 35 = 560; n = 15 [1] correct proportion solved incorrectly 55. [4] a. b.  = x = 4.8 cm = y = 7.5 cm n + 1 28 20 35 x 4 6 5 6 4 y 5 8-5

Proportions in Triangles GEOMETRY LESSON 8-5 65. RT = SV = 48 66. RT = SV = 6.5 55. (continued) [3] correct drawings and proportions with one computational error [2] one possibility drawn and done correctly OR two correct drawings [1] one correct drawing OR one correct proportion 56. m 57. m 58. c 59. h 60. x = 24; y = 12 3 61. x = 9; y = 9 3 62. x = 15; y = 30 63. RT = SV = 38 64. RT = SV = 37 8-5